Series and Parallel Elements Equivalent Resistance

Series and Parallel Elements Two or more elements are in series if they are cascaded or connected sequentially and consequently carry the same current through them. Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them.

Series Resistors The equivalent resistance of any number of resistors connected in series is the sum of the individual resistances.

Voltage Division To determine the voltage across each resistor we use: The voltage is divided among the resistors in direct proportion to their resistances.

Parallel Resistors The equivalent resistance of two parallel resistors is equal to the product of their resistances divided by their sum.

Parallel Resistors (cont.) The equivalent resistance of N resistors in parallel is Req is always smaller than the resistance of the smallest resistor in the parallel combination. If the resistances are equal, simply divide by the number of resistors.

Parallel Conductance It is often more convenient to use conductance when dealing with parallel resistors. The equivalent conductance of resistors connected in parallel is the sum of their individual conductances.

Serial Conductance The equivalent conductance of series resistors is obtained in the same manner as the resistance of resistors in parallel.

Current Division For two resistors in parallel, the resistors will have current

Current Division (cont.) The total current i is shared by the resistors in inverse proportion to their resistances. If a current divider has N conductors in parallel, the nth conductor (Gn) will have current

Examples Find Req by combining the resistors.

Examples Calculate the equivalent resistance Rab in the circuit.

Examples Find the equivalent conductance Geq for the circuit.

Examples Find the currents and voltages in the circuit.